PERTURBATIVE SOLUTIONS OF DIFFERENTIAL EQUATIONS IN LIE GROUPS
2005 ◽
Vol 02
(01)
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pp. 111-125
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We show that, given a matrix Lie group [Formula: see text] and its Lie algebra [Formula: see text], a 1-parameter subgroup of [Formula: see text] whose generator is the sum of an unperturbed matrix Â0 and an analytic perturbation Â♢(λ) can be mapped — under suitable conditions — by a similarity transformation depending analytically on the perturbative parameter λ, onto a 1-parameter subgroup of [Formula: see text] generated by a matrix [Formula: see text] belonging to the centralizer of Â0 in [Formula: see text]. Both the similarity transformation and the matrix [Formula: see text] can be determined perturbatively, hence allowing a very convenient perturbative expansion of the original 1-parameter subgroup.
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2009 ◽
Vol 19
(03)
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pp. 337-345
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1994 ◽
Vol 46
(2)
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pp. 438-448
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2011 ◽
Vol 148
(3)
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pp. 807-834
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2009 ◽
Vol 146
(2)
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pp. 351-378
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1957 ◽
Vol 64
(3)
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pp. 290-304
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